The maximum output current of the Vcc regulator is 100mA, therefore for a 4.7Ω resistor the maximum power loss across would be 47mW. Any resistor with a power rating ~1.5 times greater than this value is acceptable.
MAX16814
Production
The MAX16814 high-efficiency, high-brightness LED (HB LED) driver provides up to four integrated LED current-sink channels. An integrated current-mode...
Datasheet
MAX16814 on Analog.com
The maximum output current of the Vcc regulator is 100mA, therefore for a 4.7Ω resistor the maximum power loss across would be 47mW. Any resistor with a power rating ~1.5 times greater than this value is acceptable.